Given a finite set in a metric space, the topological analysis generalizes hierarchical clustering using a 1-parameter family of homology groups to quantify connectivity in all dimensions. Going beyond Euclidean distance and really beyond metrics, we show that the tools of topological data analysis also apply when we measure distance with Bregman divergences. While these divergences violate two...

We propose an information complexity-based regularization parameter selection method for solution of ill-conditioned inverse problems. The regularization parameter is selected to be the minimizer of the Kullback-Leibler (KL) distance between the unknown data-generating distribution and the fitted distribution. The KL distance is approximated by an information complexity (ICOMP) criterion develo...

Deconvolution is usually regarded as one of the so called ill-posed problems of applied mathematics if no constraints on the unknowns can be assumed. In this paper, we discuss the idea of well-de ned statistical models being a counterpart of the notion of well-posedness. We show that constraints on the unknowns such as non-negativity and sparsity can help a great deal to get over the inherent i...

In this paper, we propose a Generalized Approximate Cross Validation (GACV) function for estimating the smoothing parameter in the penalized log likelihood regression problem with non-Gaussian data. This GACV is obtained by, first, obtaining an approximation to the leaving-out-one function based on the negative log likelihood, and then, in a step reminiscent of that used to get from leaving-out...

We propose a stochastic framework to analyze and compare differences in human motions for applications in injury prevention, rehabilitation, sports training and performance research. Human motions are modeled as Hidden Markov Models and the differences between the motions are measured using the Kullback-Leibler distance metric. The distance metric is recomputed with degrees of freedom excluded ...

In this paper, we describe two approaches to the problem of encoding cortical waves of turtle visual cortex. The first approach relies on representing the response of individual pyramidal cells using various temporal scales (multiresolution analysis). In the second approach, we consider decomposing the visual cortex into various spatial grids. Each of these spatial grid contains several neurons...

An extension of the switching-state models (SSSM) that allows arbitrary number of components is presented. We introduce a Dirichlet process prior over the mixture components of the linear models. This prior allows the inference on the number of linear models to be put into the mixture. We develop a distance measure in the space of linear Kalman filters with the use of the Kullback-Leibler diver...

In this paper we investigate distance functions on finite state Markov processes that measure the behavioural similarity of non-bisimilar processes. We consider both probabilistic bisimilarity metrics, and tracebased distances derived from standard Lp and Kullback-Leibler distances. Two desirable continuity properties for such distances are identified. We then establish a number of results that...

Images obtained from coherent illumination processes are contaminated with speckle. A prominent example of such imagery systems is the polarimetric synthetic aperture radar (PolSAR). For such remote sensing tool the speckle interference pattern appears in the form of a positive definite Hermitian matrix, which requires specialized models and makes change detection a hard task. The scaled comple...

For the application of many statistical methods it is necessary to establish the measure of di erence to be used This measure has to be de ned in accordance with the nature of the data In this study we propose a measure of di erence when the data set is compositional We analyze its properties and we present examples to illustrate its performance INTRODUCTION It is well known that the usual diss...